Nielsen And Chuang Solutions Manual

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Let $S= langle g_1, g_2, cdots, g_l rangle $ be a subgroup of a $n-$fold Pauli group $P_n$ generated by $g_1, g_2, cdots, g_l$. Exercise 10.34 in Nielsen & Chuang requires to show that $S$ does not contain $-I$ if and only if $g_i ^2 = I $ and $g_i ne -I$ for all $i=1,2, cdots,l$.

The 'only if' part is not difficult, but I have a trouble with the 'if' part. How can I show that $S= langle g_1, g_2, cdots, g_l rangle $ does not contain $-I$ if $g_i ^2 = I $ and $g_i ne -I$ for all $i=1,2, cdots,l$?

This text is refreshing if you want a lot of worked examples to help you through another text like, (Quantum Computation and Quantum Information, Michael A. Nielsen, Isaac L. Chuang, ISBN: ). I was excited when this text came out and had an order in before it got off the press. When I got the book I immediately.